Properties of wavelet estimates of signals recorded at random time points

Wavelet analysis algorithms in combination with threshold processing procedures are widely used in nonparametric regression problems when estimating the signal function from noisy data. The advantages of these methods are their computational efficiency and the ability to adapt to the local features of the function being estimated. The error analysis of threshold processing methods is an important practical task, since it allows assessing the quality of both the methods themselves and the equipment used. Sometimes, the nature of the data is such that observations are recorded at random times. If the sampling points form a variation series constructed from a sample of a uniform distribution over the data recording interval, then the use of conventional threshold processing procedures is adequate. In this paper, the author analyzes the estimate of the mean square risk of threshold processing and shows that under certain conditions, this estimate is strongly consistent and asymptotically normal.